Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores I. Spectral energy distributions and evolutionary sequence

Context. The low-mass star formation evolutionary sequence is relatively well-defined both from observations and theoretical considerations. The first hydrostatic core is the first protostellar equilibrium object that is formed during the star formation process. Aims. Using state-of-the-art radiation-magneto-hydrodynamic 3D adaptive mesh refinement calculations, we aim to provide predictions for the dust continuum emission from first hydrostatic cores. Methods. We investigated the collapse and the fragmentation of magnetized 1 M-circle dot prestellar dense cores and the formation and evolution of first hydrostatic cores using the RAMSES code. We used three different magnetization levels for the initial conditions, which cover a wide variety of early evolutionary morphology, e. g., the formation of a disk or a pseudo-disk, outflow launching, and fragmentation. We post-processed the dynamical calculations using the 3D radiative transfer code RADMC-3D. We computed spectral energy distributions and usual evolutionary stage indicators such as bolometric luminosity and temperature. Results. We find that the first hydrostatic core lifetimes depend strongly on the initial magnetization level of the parent dense core. We derive, for the first time, spectral energy distribution evolutionary sequences from high-resolution radiation-magneto-hydrodynamic calculations. We show that under certain conditions, first hydrostatic cores can be identified from dust continuum emission at 24 mu m and 70 mu m. We also show that single spectral energy distributions cannot help in distinguishing between the formation scenarios of the first hydrostatic core, i.e., between the magnetized and non-magnetized models. Conclusions. Spectral energy distributions are a first useful and direct way to target first hydrostatic core candidates but high-resolution interferometry is definitively needed to determine the evolutionary stage of the observed sources.